Universal upper bound on the entropy-to-energy ratio for bounded systems
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...The entropy bounds discussed in this section are “universal” (Bekenstein, 1981) in the sense that they are independent of the specific characteristics and composition of matter systems....
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...oblem, as one may define R in terms of the surface area. A Schwarzschild black hole in four dimensions has R = 2E. Hence, its Bekenstein entropy, S = A/4 = πR2, exactly saturates the Bekenstein bound (Bekenstein, 1981). In D > 4, black holes come to within a factor 2 D−2 of saturating the bound (Bousso, 2001). 10 C. Spherical entropy bound Instead of dropping a thermodynamic system into an existing black hole vi...
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...(2.9), has much empirical support (Bekenstein, 1981, 1984; Schiffer and Bekenstein, 1989)....
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...Hence, its Bekenstein entropy, S = A/4 = πR2, exactly saturates the Bekenstein bound (Bekenstein, 1981)....
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... one would not expect quantum buoyancy to play a crucial role. 3. Empirical status Independently of its logical relation to the GSL, one can ask whether the Bekenstein bound actually holds in nature. Bekenstein (1981, 1984) and Schiffer and Bekenstein (1989) have made a strong case that all physically reasonable, weakly gravitating matter systems satisfy Eq. (2.9); some come within an order of magnitude of saturat...
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